关键词:
Fractional (p, q)-Laplacian problem
Kirchhoff type problem
Penalization technique
Lusternik-Schnirelman theory
摘要:
In this paper, we deal with the following class of fractional (p, q)-Laplacian Kirchhoff type problem: {(1 + [u](s,p)(p)) (-Delta)(p)(s)u + (1 + [u](s,q)(q)) (-Delta)(q)(s)u + V (epsilon x) (vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(q-2)u) = f(u) in R-N, u is an element of W-s,W-p (R-N) boolean AND W-s,W-q (R-N), u > 0 in R-N, where epsilon > 0, s is an element of (0, 1), 1 < p < q < N/s < 2q, (-Delta)(t)(s), with t is an element of {p, q}, is the fractional t-Laplacian operator, V : R-N -> R is a positive continuous potential such that inf(partial derivative)(Lambda) V > inf(Lambda )V for some bounded open set Lambda subset of R-N, and f : R -> R is a superlinear continuous nonlinearity with subcritical growth at infinity. By combining the method of Nehari manifold, a penalization technique, and the Lusternik-Schnirelman category theory, we study the multiplicity and concentration properties of solutions for the above problem when epsilon -> 0.